(x^2-9)(4x^2-1)=0

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Solution for (x^2-9)(4x^2-1)=0 equation: 


Simplifying
(x2 + -9)(4x2 + -1) = 0

Reorder the terms:
(-9 + x2)(4x2 + -1) = 0

Reorder the terms:
(-9 + x2)(-1 + 4x2) = 0

Multiply (-9 + x2) * (-1 + 4x2)
(-9(-1 + 4x2) + x2(-1 + 4x2)) = 0
((-1 * -9 + 4x2 * -9) + x2(-1 + 4x2)) = 0
((9 + -36x2) + x2(-1 + 4x2)) = 0
(9 + -36x2 + (-1 * x2 + 4x2 * x2)) = 0
(9 + -36x2 + (-1x2 + 4x4)) = 0

Combine like terms: -36x2 + -1x2 = -37x2
(9 + -37x2 + 4x4) = 0

Solving
9 + -37x2 + 4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x2)(9 + -1x2) = 0

Factor a difference between two squares.
((1 + 2x)(1 + -2x))(9 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(1 + 2x)(1 + -2x) = 0


Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

Subproblem 4
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 0.5, -3, 3}

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